Model-based system and method for mitigating diesel emission fluid deposits

ABSTRACT

A system and method for mitigating deposit of diesel emission fluid (DEF) decomposition products on interior surfaces of an internal combustion engine exhaust system ( 14 ). A processor in a controller ( 34 ) contains a model-based control algorithm ( 50 A;  50 B) for controlling DEF injection by a DEF injector ( 24 ) to mitigate deposit formation.

TECHNICAL FIELD

This disclosure relates to internal combustion engines, especially diesel engines like those used to propel large trucks, and in particular the disclosure relates to engine exhaust after-treatment that comprises injecting diesel emission fluid (DEF), such as a urea solution, into an engine exhaust system for promoting selective catalytic reduction (SCR) of certain constituents, NOx for example, in engine exhaust.

BACKGROUND OF THE DISCLOSURE

An example of a diesel engine exhaust after-treatment system that uses selective catalytic reduction comprises an injector through which DEF is injected into the exhaust flow. DEF is a solution that either comprises, or as it entrains with the exhaust flow is converted into, one or more constituents that promote catalytic action that treats certain exhaust constituents such as NOx. Ideally DEF should completely vaporize and thoroughtly mix with the exhaust before the flow passes across catalytic surfaces.

The geometry of an exhaust after-treatment system and the spray pattern of a DEF injector may cause some of the injected DEF to wet interior surfaces of the exhaust system before it vaporizes. When the temperature of those surfaces is low enough, a potential exists for solute (urea for example) to come out of solution and form deposits on those surfaces. Accumulations of solid deposits may, over time, impair the effectiveness of the after-treatment system, such as by altering flow characteristics of the exhaust and/or the spray pattern of the injector, and/or they may damage exhaust and after-treatment system components.

Removal of significant deposits typically requires disassembly of components because of lack of acceptable ways to satisfactorily remove them without such disassembly.

In order to avoid wetting surfaces that are cold enough to cause solute to precipitate out of solution and deposit on those surfaces, an injection of DEF may be temporarily delayed when a cold engine is first started, especially during cold ambient conditions. That delay however postpones the onset of SCR treatment of the exhaust.

SUMMARY OF THE DISCLOSURE

The present disclosure provides a system and method for mitigating the potential for formation of DEF deposits in an engine exhaust system.

A general aspect of the disclosure relates to a control system, in a vehicle that is propelled by an internal combustion engine, for mitigating deposit of decomposition products of diesel emission fluid (DEF) on an interior of an exhaust system through which exhaust is flowing from the engine toward a catalyst that promotes chemical reaction between a constituent in the exhaust and a constituent that has become entrained in the exhaust as a consequence of injection of DEF from a DEF injector.

The system comprises a processor containing a model-based control algorithm for controlling an aspect of DEF injection by the DEF injector, the control algorithm comprising a model that models convective heat transfer from the exhaust to a given area of an interior surface of the exhaust system that is separated from an exterior surface in contact with atmospheric air by material of the exhaust system, conductive heat transfer from the given area to any liquid DEF on the given area, conductive heat transfer through the material of the exhaust system to the exterior surface, and convective heat transfer from the exterior surface to atmospheric air.

The processor comprises an operating routine that: processes data relating to the exhaust and to atmospheric air that affect the convective and conductive heat transfers according to the model to calculate temperature (T_(in wall)) of the given area of the interior surface; that compares the calculated temperature (T_(in wall)) of the given area of the interior surface and a temperature (T_(crit)) below which liquid DEF on the given area has potential to deposit solid material on the given area, and that uses the result of the comparison to control DEF injection by the DEF injector.

Another general aspect of the disclosure relates to a method for mitigating deposit of decomposition products of diesel emission fluid (DEF) on an interior of an exhaust system through which exhaust is flowing from a motor vehicle internal combustion engine toward a catalyst which promotes chemical reaction between a constituent in the exhaust and a constituent that has become entrained in the exhaust as a consequence of injection of DEF into the exhaust system by a DEF injector.

The method comprises using a processor to control an aspect of injection of DEF by the DEF injector by repeatedly executing in the processor a model-based control algorithm comprising a model that models convective heat transfer from the exhaust to a given area of an interior surface of the exhaust system that is separated from an exterior surface in contact with atmospheric air by material of the exhaust system, conductive heat transfer from the given area to any liquid DEF on the given area, conductive heat transfer through the material of the exhaust system to the exterior surface, and convective heat transfer from the exterior surface to atmospheric air.

Executing the model-based control algorithm comprises processing data relating to the exhaust and to atmospheric air that affect the convective and conductive heat transfers to calculate temperature (T_(in wall)) of the given area of the interior surface, comparing the calculated temperature (T_(in wall)) of the given area of the interior surface and a temperature (T_(crit)) below which liquid DEF on the given area has potential to deposit solid material on the given area, and using the result of the comparison to control injection of DEF by the DEF injector.

Another general aspect of the disclosure relates to a control system, in a vehicle that is propelled by an internal combustion engine, for mitigating deposit of decomposition products of diesel emission fluid (DEF) on an interior of an exhaust system through which exhaust is flowing from the engine toward a catalyst that promotes chemical reaction between a constituent in the exhaust and a constituent that has become entrained in the exhaust as a consequence of injection of DEF from a DEF injector.

The system comprises a processor containing a model-based control algorithm for controlling an aspect of DEF injection by the DEF injector, the control algorithm comprising a model that models convective heat transfer from the exhaust to a given area of an interior surface of the exhaust system that is separated from an exterior surface in contact with atmospheric air by material of the exhaust system, conductive heat transfer from the given area to any liquid DEF on the given area, conductive heat transfer through the material of the exhaust system to the exterior surface, and convective heat transfer from the exterior surface to atmospheric air.

The processor comprises an operating routine that: processes, according to the model, data relating to the exhaust and to atmospheric air that affect the convective and conductive heat transfers to calculate a desired flow rate for injection of DEF by the DEF injector; that selects, for the actual flow rate for DEF injected by the DEF injector, the lower of a flow rate based on a temperature of the given area of the interior surface below which liquid DEF on the given area has potential to deposit solid material on the given area and the desired flow rate calculated according to the model; and that uses the result of the selection to set the actual flow rate of injection of DEF by the DEF injector.

Another general aspect of the disclosure relates to a method for mitigating deposit of decomposition products of diesel emission fluid (DEF) on an interior of an exhaust system through which exhaust is flowing from a motor vehicle internal combustion engine toward a catalyst which promotes chemical reaction between a constituent in the exhaust and a constituent that has become entrained in the exhaust as a consequence of injection of DEF into the exhaust system by a DEF injector.

The method comprises using a processor to control an aspect of injection of DEF by the DEF injector by repeatedly executing in the processor a model-based control algorithm comprising a model that models convective heat transfer from the exhaust to a given area of an interior surface of the exhaust system that is separated from an exterior surface in contact with atmospheric air by material of the exhaust system, conductive heat transfer from the given area to any liquid DEF on the given area, conductive heat transfer through the material of the exhaust system to the exterior surface, and convective heat transfer from the exterior surface to atmospheric air.

Executing the model-based control algorithm comprises: processing, according to the model, data relating to the exhaust and to atmospheric air that affect the convective and conductive heat transfers to calculate a desired flow rate for injection of DEF by the DEF injector; selecting, for the actual flow rate of DEF injected by the DEF injector, the lower of a flow rate based on a temperature of the given area of the interior surface below which liquid DEF on the given area has potential to deposit solid material on the given area and the desired flow rate calculated according to the model; and using the result of the selection to set the actual flow rate of injection of DEF by the DEF injector.

The foregoing summary, accompanied by further detail of the disclosure, will be presented in the Detailed Description below with reference to the following drawings that are part of this disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a general schematic diagram of an engine and its exhaust system, including after-treatment.

FIG. 2 is a more detailed schematic diagram of exhaust after-treatment useful in understanding the disclosed model-based system and method.

FIG. 3 is a first embodiment of DEF injection control algorithm.

FIG. 4 is a second embodiment of DEF injection control algorithm.

DETAILED DESCRIPTION

FIG. 1 shows an example of a turbocharged diesel engine 10 having an intake system 12 through which charge air enters and an exhaust system 14 through which exhaust gas resulting from combustion exits, not all details of those two systems that are typically present being shown. Engine 10 comprises a number of cylinders 16 forming combustion chambers into which fuel is injected by fuel injectors to combust with the charge air that has entered through intake system 12. Energy released by combustion powers the engine via pistons connected to a crankshaft.

When used in a motor vehicle, such as a truck, engine 10 is coupled through a drivetrain to driven wheels that propel the vehicle. Intake valves control the admission of charge air into cylinders 16, and exhaust valves control the outflow of exhaust through exhaust system 14 and ultimately to atmosphere. Before entering the atmosphere however, the exhaust is treated by one or more after-treatment devices in an after-treatment portion of exhaust system 14.

After-treatment portion of exhaust system 14 comprises a walled enclosure 18 circumscribing an exhaust flow path through which exhaust from cylinders 16 passes. The interior of enclosure 18 contains a diesel particulate filter (DPF) 20 and a mixer 22 downstream of DPF 20.

A DEF injector 24 is mounted in a boss 26 on the wall of enclosure 18 for spraying DEF from a nozzle 28 into exhaust flowing along the exhaust flow path. Flow that has passed through mixer 22 subsequently passes across catalytic surfaces of an SCR catalyst 30 that promotes treatment of an exhaust constituent by a chemical in the DEF and/or a decomposition product of a chemical in the DEF before the flow exits exhaust system 14 through a tailpipe.

A supply of DEF is stored in a tank 32. An example of a DEF is an aqueous urea solution that has approximately a 32.5% concentration by weight and that can reduce NOx in exhaust.

The injection of DEF into the exhaust flow is controlled by execution of a DEF injection control algorithm in a controller 34 that is associated with the supply in tank 32 and with injector 24. FIG. 1 shows an example of an exhaust system design in which injector nozzle 28 lies substantially on an imaginary centerline aimed downstream of the exhaust flow, but at an acute angle to the prevailing axial direction of flow coming from DPF 20 to inject DEF as a spray 36 that contains droplets small enough to completely vaporize in exhaust that is sufficiently hot. The reference numeral 36 depicts the spray pattern only generally and is not intended to imply that it will necessarily strike wall 18 or any other portions of the exhaust system.

Mixer 22 is intended to promote thorough mixing of the DEF with the exhaust flow during transit to SCR catalyst 30 which comprises catalytic surfaces for promoting the reaction of exhaust with product(s) in, and/or decomposition product(s) of product(s) in, vaporized DEF. Mixer 22 can promote the vaporization of any DEF droplets that may strike it and decomposition of urea.

FIG. 2 shows that the wall of enclosure 18 comprises an interior surface 40 and an exterior surface 42. A sensor 44 senses temperature of exhaust that flows through enclosure 18 in the sense indicated by the arrow labeled “Exhaust”. An area of interior surface 40 lies within the pattern of spray 36. Limited vaporization of injected DEF occurs in the exhaust and consequently some droplets will impinge on internal exhaust system surfaces. If those surfaces are sufficiently hot, the impinging DEF will quickly evaporate. Sufficiently quick evaporation does not lead to surface wetting that can create deposits.

When the temperature of interior surface 40 is greater than the temperature of droplets wetting the surface, heat will transfer from the wall to the droplets to vaporize them as indicated by the arrow labeled H DEF_(vap).

A parameter Q_(in) represents thermal energy (heat) input to the area of interior surface 40 in the path of spray 36. Assuming that the temperature of interior surface 40 is greater than that of exterior surface 42, a quantity of heat Q_(thru) will be conducted through the wall of enclosure 18 to exterior surface 42. Assuming that the temperature of exterior surface 42 is greater than that of atmospheric air that is in contact with exterior surface 42, then a quantity of heat Q out will be transferred to the air.

The equations that follow describe relevant relationships assuming one-dimensional, steady-state heat transfer and neglecting radiation.

Convective heat transfer from exhaust to interior surface 40 may be described by the equation:

Q _(in) =h _(in)×(T _(exh) −T _(in wall))

-   -   where h_(in) is the convective heat transfer coefficient for         heat transfer from the exhaust to interior surface 40 (based on         sensor measurements, empirical data, and calculations),     -   T_(exh) is temperature of the exhaust gas as measured by sensor         44, and     -   T_(in wall) is the temperature of interior surface 40 and is         described by the equation:

T _(in wall) =K ₁ ×T _(amb) +K ₂ ×T _(exh) −K ₃ ×m _(DEF)

-   -   where

K ₁=1/(1+h _(in) /k _(ext))

K ₂=1/(1+k _(ext) /h _(in))

K ₃ =h _(DEFvap)/(h _(in) +k _(ext))

-   -   and T_(amb) is the temperature of atmospheric air (based on         sensor measurements),     -   m_(DEF) is the flow rate of DEF being injected by injector 24         (based on sensor measurements, empirical data, & calculations).

h_(DEFvap) is the heat of vaporization (and decomposition, if any) of DEF, and

k_(ext) is described by the equation:

k _(ext) =k _(wall) ×h _(out)/(k _(wall) +h _(out))

-   -   where k_(wall) is i the thermal conductivity of the wall of         enclosure 18, and     -   h_(out) is the convective heat transfer coefficient from         exterior surface 42 to atmospheric air (based on sensor         measurements, empirical data, & calculations).

If no liquid DEF is on interior surface 40, then all heat transferred from the exhaust to interior surface 40 (Q_(in)) will be transferred through the wall of enclosure 18 to exterior surface 42.

However, if liquid DEF is present on interior surface 40, only a portion of Q_(in) will be transferred through the wall of enclosure 18 to exterior surface 42 and the remainder will vaporize, and possibly also decompose, the DEF. This condition is described by the equation:

Q _(in) =Q _(thru) +H _(DEFvap)

-   -   where Q_(thru) is the heat transferred through the wall of         enclosure 18 to exterior surface 42 and H_(DEFvap) is heat         transferred to liquid DEF present on interior surface 40.

The last equation may be expanded to:

Q _(in) =k _(wall)×(T _(in wall) −T _(out wall))+m _(DEF) ×h _(DEFvap)

Convective heat transfer from exterior surface 42 to atmospheric air is described by:

Q _(out) =h _(out)×(T _(out wall) −T _(amb))

-   -   where h_(out) is the convective heat transfer coefficient for         heat transfer from exterior surface 42 to atmospheric air (based         on sensor measurements, empirical data, and calculations), and         T_(out wall) is the temperature of exterior surface 42.

A parameter T_(crit) represents a temperature below which the liquid phase of a particular DEF on a surface have the potential to form deposits on that surface.

By calculating the temperature T_(in wall) using the above equation and then comparing the result to T_(crit), it can be determined if the temperature of interior surface 40 is high enough to avoid liquid DEF forming deposits on the surface.

The calculation of temperature T_(in wall) utilizes the constants, h_(DEFvap) and k_(wall) and the variables h_(in), h_(out), T_(amb), T_(exh), and m_(DEF). The parameter h_(in) is a variable because it is a function of the rate of exhaust flow through enclosure 18. Parameter h_(out) is a variable because it is a function of the rate of air flow along exterior surface 42.

FIG. 1 shows various input data, represented generally by reference numeral 38, are processed by the DEF injection control algorithm in controller 34, a first embodiment 50A of which is shown in FIG. 3.

DEF injection control algorithm 50A comprises certain processing steps, a first one of which (step 52) determines if a present value for DEF flow rate m_(def) needs to be updated. After that, a second step 54 is performed to calculate energy balance and a temperature T_(in wall) of interior wall surface 40. After that, a third step 56 is performed to compare T_(in wall) with a temperature T_(crit) representing a temperature of the area of interior surface 40 in the path of spray 36 below which liquid DEF on the area have potential to deposit solid material on the area.

In performing its calculation, step 54 processes data 57 representing temperature and atmospheric pressure of ambient air, data 58 representing speed at which a vehicle that is being propelled by engine 10 is traveling (this affects air flow along exterior surface 42), data 60 representing temperature of engine exhaust at any suitable location in exhaust system 14, typically upstream of injector 24 but downstream of DPF 20, as provided by sensor 44, and data 62 representing flow rate of engine exhaust. Data 57, 58, 60, and 62 are all variables. Engine speed data 70 and engine fueling data 72 are used to calculate flow rate of engine exhaust.

Additional data 64, 66, 68 are also processed by step 54. Data 64, 66, and 68 are typically non-variable for a given exhaust and after-treatment system and can therefore be embedded in controller 34. Data 64 defines certain thermodynamic properties of atmospheric air. Data 66 defines certain properties of walled enclosure 18 relevant to heat transfer through its wall between interior surface 40 across which exhaust flows and exterior surface 42 that is in contact with atmospheric air. Data 68 defines certain thermodynamic properties of the particular DEF that is injected by injector 24.

The algorithm routine comprises:

Calculating T_(in wall)

If T_(in wall)>T_(crit) injecting DEF at m_(def) (step 98 in FIG. 3)

If T_(in wall)≦T_(crit), then reducing m_(def) until T_(in wall)>T_(crit) (step 100 in FIG. 3) and injecting DEF at the reduced m_(def).

If the reduced m_(def)≦0, stopping injection of DEF, until

T_(in wall)>T_(crit).

FIG. 4 shows another DEF injection control algorithm 50B that comprises processing steps 90, 92, 94, and 98. Each iteration of step 90 calculates a desired flow rate for injection of DEF by DEF injector 24 m_(DEF) for securing optimum performance of SCR catalyst 30, by rearranging the above equation for T_(in wall) the equation:

m _(DEF)=(T _(in wall) −K1×T _(amb) −K2×T _(exh))/K3

If an iteration produces a result different from that of an immediately preceding iteration, then the value of m_(DEF) is updated (step 92).

Step 94 calculates energy balance and a parameter m_(DEFcrit) where

m _(DEFcrit)=(T _(crit) −K1×T _(amb) −K2×T _(exh))/K3

If the calculated value for m_(DEF) is not too high for the temperature T_(in wall), meaning that deposits will not form, then that calculated value is used instead of m_(DEFcrit) to set the actual flow rate of DEF injected by DEF injector 24. On the other hand, if the calculated value for m_(DEF) is too high for the temperature T_(wall), meaning that deposits can form, then m_(DEFcrit) is used to set the actual flow rate of DEF injected by DEF injector 24. The selection of which is lower, m_(DEF) or m_(DEFcrit), is made by step 98, and it is that selected value which is used as the actual flow rate of DEF injection. 

What is claimed is:
 1. A control system, in a vehicle that is propelled by an internal combustion engine, for mitigating deposit of decomposition products of diesel emission fluid (DEF) on an interior of an exhaust system through which exhaust is flowing from the engine toward a catalyst that promotes chemical reaction between a constituent in the exhaust and a constituent that has become entrained in the exhaust as a consequence of injection of DEF from a DEF injector, the system comprising: a processor containing a model-based control algorithm for controlling an aspect of DEF injection by the DEF injector, the control algorithm comprising a model that models convective heat transfer from the exhaust to a given area of an interior surface of the exhaust system that is separated from an exterior surface in contact with atmospheric air by material of the exhaust system, conductive heat transfer from the given area to any liquid DEF on the given area, conductive heat transfer through the material of the exhaust system to the exterior surface, and convective heat transfer from the exterior surface to atmospheric air, the processor comprising an operating routine that: processes data relating to the exhaust and to atmospheric air that affect the convective and conductive heat transfers according to the model to calculate temperature (T_(in wall)) of the given area of the interior surface, that compares the calculated temperature (T_(in wall)) of the given area of the interior surface and a temperature (T_(crit)) below which liquid DEF on the given area has potential to deposit solid material on the given area, and that uses the result of the comparison to control DEF injection by the DEF injector.
 2. A control system as set forth in claim 1 in which the model models convective heat transfer from the exhaust to the given area of an interior surface of the exhaust system (Q_(in)) by the equation: Q _(in) =h _(in)×(T _(exh) −T _(in wall)) where h_(in) is the convective heat transfer coefficient for heat transfer from the exhaust to the given area of the interior surface, and T_(exh) is temperature of the exhaust.
 3. A control system as set forth in claim 2 in which the model models T_(in wall) by the equation: T _(in wall) =K ₁ ×T _(amb) +K ₂ ×T _(exh) −K ₃ ×m _(DEF) where K ₁=1/(1+h _(in) /k _(ext)) K ₂=1/(1+k _(ext) /h _(in)) K ₃ =h _(DEFvap)/(h _(in) +k _(ext)) and T_(amb) is the temperature of atmospheric air, m_(DEF) is the flow rate of DEF being injected by the DEF injector, h_(DEFvap) is the heat of vaporization and any decomposition of DEF, and k_(ext) is described by the equation: k _(ext) =k _(wall) ×h _(out)/(k _(wall) +h _(out)) where k_(wall) is the thermal conductivity of the material of the exhaust system, and h_(out) is the convective heat transfer coefficient for heat transfer from the exterior surface to atmospheric air.
 4. A control system as set forth in claim 1 in which, when the result of the comparison of T_(in wall) with T_(crit) determines that liquid DEF on the given area has potential to deposit solid material on the given area, the model models convective heat transfer from the exhaust to the given area of the interior surface (Q_(in)) by the equation, Q _(i) =k _(wall)×(T _(in wall) −T _(out wall))+m _(DEF) ×h _(DEFvap) and convective heat transfer from the external surface to atmospheric air (Q_(out)) by the equation, Q _(out) =h _(out)×(_(T) _(out wall) −T _(amb)) where k_(wall) is the thermal conductivity of the material of the exhaust system, T_(out wall) is temperature of the exterior surface, m_(DEF) is the flow rate of DEF being injected by the DEF injector, h_(DEFvap) is the heat of vaporization and any decomposition of DEF, h_(out) is the convective heat transfer coefficient for heat transfer from the exterior surface to atmospheric air, and T_(amb) is the temperature of atmospheric air.
 5. A control system as set forth in claim 1 in which the operating routine reduces the flow rate at which DEF is being injected by the DEF injector when T_(in wall)≦T_(crit), continues reducing the flow rate at which DEF is being injected by the DEF injector until T_(in wall)>T_(crit), and when the flow rate at which DEF is being injected by the DEF injector ≦0, stops injection of DEF by the DEF injector until T_(in wall)>T_(crit) whereupon injection of DEF by the DEF injector is resumed.
 6. A control system as set forth in claim 1 in which the data relating to the exhaust and to atmospheric air that affect the convective and conductive heat transfers include at least temperature of exhaust, flow rate of exhaust, temperature of atmospheric air, and speed of a vehicle that is equipped with the control system.
 7. A method for mitigating deposit of decomposition products of diesel emission fluid (DEF) on an interior of an exhaust system through which exhaust is flowing from a motor vehicle internal combustion engine toward a catalyst which promotes chemical reaction between a constituent in the exhaust and a constituent that has become entrained in the exhaust as a consequence of injection of DEF into the exhaust system by a DEF injector, the method comprising: using a processor to control an aspect of injection of DEF by the DEF injector by repeatedly executing in the processor a model-based control algorithm comprising a model that models convective heat transfer from the exhaust to a given area of an interior surface of the exhaust system that is separated from an exterior surface in contact with atmospheric air by material of the exhaust system, conductive heat transfer from the given area to any liquid DEF on the given area, conductive heat transfer through the material of the exhaust system to the exterior surface, and convective heat transfer from the exterior surface to atmospheric air, in which executing the model-based control algorithm comprises processing data relating to the exhaust and to atmospheric air that affect the convective and conductive heat transfers to calculate temperature (T_(in wall)) of the given area of the interior surface, comparing the calculated temperature (T_(in wall)) of the given area of the interior surface and a temperature (T_(crit)) below which liquid DEF on the given area has potential to deposit solid material on the given area, and using the result of the comparison to control injection of DEF by the DEF injector.
 8. A method as set forth in claim 7 in which the model models convective heat transfer from the exhaust to the given area of an interior surface of the exhaust system (Q_(in)) by calculating: h _(in)×(T _(exh) −T _(in wall)) where h_(in) is the convective heat transfer coefficient for heat transfer from the exhaust to the given area of the interior surface, T_(exh) is temperature of exhaust, and T_(in) wall is temperature of the given area of the interior surface.
 9. A method as set forth in claim 8 in which the model models temperature of the given area of the interior surface T_(in wall) by calculating: T _(in wall) =K ₁ ×T _(amb) +K ₂ ×T _(exh) −K ₃ ×m _(DEF) where K ₁=1/(1+h _(in) /k _(ext)) K₂=1/(1+k _(ext) /h _(in)) K ₃ =h _(DEFvap)/(h _(in) +k _(ext)) and T_(amb) is the temperature of atmospheric air, m_(DEF) is the flow rate of DEF being injected by the DEF injector, h_(DEFvap) is the heat of vaporization and any decomposition of DEF, and k_(ext) is described by the equation: k _(ext) =k _(wall) ×h _(out)(k _(wall) +h _(out)) where k_(wall) is i the thermal conductivity of the material of the exhaust system, and h_(out) is the convective heat transfer coefficient for heat transfer from the exterior surface to atmospheric air.
 10. A method as set forth in claim 7 in which, when the result of the comparison determines that liquid DEF on the given area of the interior surface has potential to cause formation of deposits on the given area of the interior surface, the model models convective heat transfer from the exhaust to the given area of the interior surface (Q_(in)) by the equation, Q _(in) =k _(wall)×(T _(in wall) −T _(out wall))+m _(DEF) ×h _(DEFvap) and convective heat transfer from the external surface to atmospheric air (Q_(out)) by the equation, Q _(out) =h _(out)×(T _(out wall)−T _(amb)) where k_(wall) is the thermal conductivity of the material of the exhaust system, T_(out wall) is temperature of the exterior surface, m_(DEF) is the flow rate of DEF being injected by the DEF injector, h_(DEFvap) is the heat of vaporization and any decomposition of DEF, h_(out) is the convective heat transfer coefficient for heat transfer from the exterior surface to atmospheric air, and T_(amb) is the temperature of atmospheric air.
 11. A method as set forth in claim 7 comprising reducing the flow rate at which DEF is being injected by the DEF injector when T_(in wall)≦T_(crit), continuing to reduce the flow rate at which DEF is being injected by the DEF injector until T_(in wall)>T_(crit), and when the flow rate at which DEF is being injected by the DEF injector ≦0, stopping injection of DEF by the DEF injector until T_(in wall)>T_(crit) when injection of DEF by the DEF injector is resumed.
 12. A method as set forth in claim 7 in which the data relating to the exhaust and to atmospheric air that affect the convective and conductive heat transfers include at least temperature of exhaust, flow rate of exhaust, temperature of atmospheric air, and speed of a motor vehicle that is propelled by the internal combustion engine and is equipped with the control system.
 13. A control system, in a vehicle that is propelled by an internal combustion engine, for mitigating deposit of decomposition products of diesel emission fluid (DEF) on an interior of an exhaust system through which exhaust is flowing from the engine toward a catalyst that promotes chemical reaction between a constituent in the exhaust and a constituent that has become entrained in the exhaust as a consequence of injection of DEF from a DEF injector, the system comprising: a processor containing a model-based control algorithm for controlling an aspect of DEF injection by the DEF injector, the control algorithm comprising a model that models convective heat transfer from the exhaust to a given area of an interior surface of the exhaust system that is separated from an exterior surface in contact with atmospheric air by material of the exhaust system, conductive heat transfer from the given area to any liquid DEF on the given area, conductive heat transfer through the material of the exhaust system to the exterior surface, and convective heat transfer from the exterior surface to atmospheric air, the processor comprising an operating routine that: processes, according to the model, data relating to the exhaust and to atmospheric air that affect the convective and conductive heat transfers to calculate a desired flow rate for injection of DEF by the DEF injector, that selects, for the actual flow rate of DEF injected by the DEF injector, the lower of a flow rate based on a temperature of the given area of the interior surface below which liquid DEF on the given area has potential to deposit solid material on the given area and the desired flow rate calculated according to the model, and that uses the result of the selection to set the actual flow rate of injection of DEF by the DEF injector.
 14. A control system as set forth in claim 13 in which the desired flow rate calculated according to the model (m_(DEF)) is modeled by the equation: m _(DEF)=(T _(in wall) −K1×T _(amb) −K2×T _(exh))/K3 and the flow rate based on a temperature of the given area of the interior surface below which liquid DEF on the given area has potential to deposit solid material on the given area (m_(DEFcrit)) is calculated by the equation: m _(DEFcrit)=(T _(crit) −K1×T _(amb) −K2×T _(exh))/K3 where K ₁=1/(1+h _(in) /k _(ext)) K ₂=1/(1+k _(ext) /h _(in)) K ₃ =h _(DEFvap)/(h _(in) +k _(ext)) T_(wall) is the temperature of the given area of the interior surface, T_(crit) is the temperature below which liquid DEF on the given area has potential to deposit solid material on the given area, T_(amb) is the temperature of atmospheric air, h_(DEFvap) is the heat of vaporization and any decomposition of DEF, and k_(ext) is described by the equation: k _(ext) =k _(wall) ×h _(out)/(k _(wall) +h _(out)) where k_(wall) is i the thermal conductivity of the material of the exhaust system, and h_(out) is the convective heat transfer coefficient for heat transfer from the exterior surface to atmospheric air.
 15. A method for mitigating deposit of decomposition products of diesel emission fluid (DEF) on an interior of an exhaust system through which exhaust is flowing from a motor vehicle internal combustion engine toward a catalyst which promotes chemical reaction between a constituent in the exhaust and a constituent that has become entrained in the exhaust as a consequence of injection of DEF into the exhaust system by a DEF injector, the method comprising: using a processor to control an aspect of injection of DEF by the DEF injector by repeatedly executing in the processor a model-based control algorithm comprising a model that models convective heat transfer from the exhaust to a given area of an interior surface of the exhaust system that is separated from an exterior surface in contact with atmospheric air by material of the exhaust system, conductive heat transfer from the given area to any liquid DEF on the given area, conductive heat transfer through the material of the exhaust system to the exterior surface, and convective heat transfer from the exterior surface to atmospheric air, in which executing the model-based control algorithm comprises: processing, according to the model, data relating to the exhaust and to atmospheric air that affect the convective and conductive heat transfers to calculate a desired flow rate for injection of DEF by the DEF injector, selecting, for the actual flow rate of DEF injected by the DEF injector, the lower of a flow rate based on a temperature of the given area of the interior surface below which liquid DEF on the given area has potential to deposit solid material on the given area and the desired flow rate calculated according to the model, and using the result of the selection to set the actual flow rate of injection of DEF by the DEF injector.
 16. A method as set forth in claim 15 in which the model models the desired flow rate (m_(DEF)) by calculating: (T _(in wall) −K1×T _(amb) −K2×T _(exh))/K3 and models the flow rate based on a temperature of the given area of the interior surface below which liquid DEF on the given area has potential to deposit solid material on the given area (m_(DEFcrit)) by calculating: (T _(crit) K1×T _(amb) −K2×T _(exh))/K3 where K ₁=1/(1+h _(in) /k _(ext)) K ₂=1/(1+k _(ext) /h _(in)) K ₃ =h _(DEFvap)/(h _(in) +k _(ext)) T_(in wall) is the temperature of the given area of the interior surface, T_(crit) is the temperature below which liquid DEF on the given area has potential to deposit solid material on the given area, T_(amb) is the temperature of atmospheric air, h_(DEFvap) is the heat of vaporization and any decomposition of DEF, and k_(ext) is described by the equation: k _(ext) =k _(wall) ×h _(out)/(k _(wall) +h _(out)) where k_(wall) is i the thermal conductivity of the material of the exhaust system, and h_(out) is the convective heat transfer coefficient for heat transfer from the exterior surface to atmospheric air. 